Tiffany Y Y Lo: An introduction to Stein’s method, with applications in random graphs

Abstract: Stein’s method is a powerful technique for bounding the error arising from approximating one distribution with another. A typical application would be proving the central limit theorem, where one can obtain an error bound for the normal approximation of the sum of (possibly dependent) random quantities. I will discuss the main concepts behind Stein’s method for Poisson and normal distributions, with classical examples in Erdös-Rényi random graphs, and more novel applications in uniform attachment random graphs.

The introductory material is based on a survey by Nathan Ross (Prob. Survey, 2011). The application in uniform attachment random graphs is based on a joint work with Johan Björklund, Cecilia Holmgren and Svante Janson.